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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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In this page, The property, Multiplication of vector is distributive over scalar addition, is explained.



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What does 'distribute' mean?distributive property illustration

  • to trouble or disturb
  • to give to many
  • to give to many

The answer is 'to give to many'.

Considering that a vector has components as real numbers, Given that `vec p = ai+bj+ck` and `lambda + mu` where `a,b,c,lambda,mu in bbb R`, What will be the result of `(lambda + mu) vec p`?Distributive property of vector multiplication by scalar

  • scalar
  • `lambda vec p + mu vec p`
  • `lambda vec p + mu vec p`
  • `lambda + mu vec p`

The answer is '`lambda vec p + mu vec p`'. This can be proven by multiplying the components individually by the scalar and using vector addition properties.

 •  A vector multiplied by sum of two scalars equals sum of the vector multiplied by the scalars.

Distributive Over scalar addition: Given scalars `lambda,mu` and vector `vec p`,
`(lambda+mu)vec p = lambda vec p + mu vec p`

Solved Exercise Problem:

Given that `vec p = 3 vec q` and `vec r = 2 vec q`, which of the following equals `7 vec q`?

  • `vec p + vec r`
  • `vec p + 2 vec r`
  • `vec p + 2 vec r`
  • `vec p - vec r`
  • `vec r - vec p`

The answer is '`vec p + 2 vec r`'

                            
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